diff -r 26983135fd6d -r 57143c09dc20 lemon/dinitz_sleator_tarjan.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/dinitz_sleator_tarjan.h	Sat Nov 17 20:58:11 2007 +0000
@@ -0,0 +1,762 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2007
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_DINITZ_SLEATOR_TARJAN_H
+#define LEMON_DINITZ_SLEATOR_TARJAN_H
+
+/// \file 
+/// \ingroup max_flow 
+/// \brief Implementation the dynamic tree data structure of Sleator
+/// and Tarjan.
+
+#include <lemon/time_measure.h>
+#include <queue>
+#include <lemon/graph_utils.h>
+#include <lemon/tolerance.h>
+#include <lemon/graph_adaptor.h>
+#include <lemon/bfs.h>
+#include <lemon/edge_set.h>
+#include <lemon/dynamic_tree.h>
+
+#include <vector>
+#include <limits>
+#include <fstream>
+
+
+namespace lemon {
+
+  /// \brief Default traits class of DinitzSleatorTarjan class.
+  ///
+  /// Default traits class of DinitzSleatorTarjan class.
+  /// \param _Graph Graph type.
+  /// \param _CapacityMap Type of capacity map.
+  template <typename _Graph, typename _CapacityMap>
+  struct DinitzSleatorTarjanDefaultTraits {
+
+    /// \brief The graph type the algorithm runs on. 
+    typedef _Graph Graph;
+
+    /// \brief The type of the map that stores the edge capacities.
+    ///
+    /// The type of the map that stores the edge capacities.
+    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
+    typedef _CapacityMap CapacityMap;
+
+    /// \brief The type of the length of the edges.
+    typedef typename CapacityMap::Value Value;
+
+    /// \brief The map type that stores the flow values.
+    ///
+    /// The map type that stores the flow values. 
+    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
+    typedef typename Graph::template EdgeMap<Value> FlowMap;
+
+    /// \brief Instantiates a FlowMap.
+    ///
+    /// This function instantiates a \ref FlowMap. 
+    /// \param graph The graph, to which we would like to define the flow map.
+    static FlowMap* createFlowMap(const Graph& graph) {
+      return new FlowMap(graph);
+    }
+
+    /// \brief The tolerance used by the algorithm
+    ///
+    /// The tolerance used by the algorithm to handle inexact computation.
+    typedef Tolerance<Value> Tolerance;
+
+  };
+
+  /// \ingroup max_flow
+  ///
+  /// \brief Dinitz-Sleator-Tarjan algorithms class.
+  ///
+  /// This class provides an implementation of the \e
+  /// Dinitz-Sleator-Tarjan \e algorithm producing a flow of maximum
+  /// value in a directed graph. The DinitzSleatorTarjan algorithm is
+  /// the fastest known max flow algorithms wich using blocking
+  /// flow. It is an improvement of the Dinitz algorithm by using the
+  /// \ref DynamicTree "dynamic tree" data structure of Sleator and
+  /// Tarjan.
+  ///
+  /// This blocking flow algorithms builds a layered graph according
+  /// to \ref Bfs "breadth-first search" distance from the target node
+  /// in the reversed residual graph. The layered graph contains each
+  /// residual edge which steps one level down. After that the
+  /// algorithm constructs a blocking flow on the layered graph and
+  /// augments the overall flow with it. The number of the levels in
+  /// the layered graph is strictly increasing in each augmenting
+  /// phase therefore the number of the augmentings is at most
+  /// \f$n-1\f$.  The length of each phase is at most
+  /// \f$O(m\log(n))\f$, that the overall time complexity is
+  /// \f$O(nm\log(n))\f$.
+  ///
+  /// \param _Graph The directed graph type the algorithm runs on.
+  /// \param _CapacityMap The capacity map type.
+  /// \param _Traits Traits class to set various data types used by
+  /// the algorithm.  The default traits class is \ref
+  /// DinitzSleatorTarjanDefaultTraits.  See \ref
+  /// DinitzSleatorTarjanDefaultTraits for the documentation of a
+  /// Dinitz-Sleator-Tarjan traits class.
+  ///
+  /// \author Tamas Hamori and Balazs Dezso
+#ifdef DOXYGEN
+  template <typename _Graph, typename _CapacityMap, typename _Traits>
+#else
+  template <typename _Graph, 
+	    typename _CapacityMap = typename _Graph::template EdgeMap<int>,
+	    typename _Traits = 
+	    DinitzSleatorTarjanDefaultTraits<_Graph, _CapacityMap> >
+#endif
+  class DinitzSleatorTarjan {
+  public:
+
+    typedef _Traits Traits;
+    typedef typename Traits::Graph Graph;
+    typedef typename Traits::CapacityMap CapacityMap;
+    typedef typename Traits::Value Value; 
+
+    typedef typename Traits::FlowMap FlowMap;
+    typedef typename Traits::Tolerance Tolerance;
+
+
+  private:
+
+    GRAPH_TYPEDEFS(typename Graph);
+
+
+    typedef typename Graph::template NodeMap<int> LevelMap;
+    typedef typename Graph::template NodeMap<int> IntNodeMap;
+    typedef typename Graph::template NodeMap<Edge> EdgeNodeMap;
+    typedef DynamicTree<Value, IntNodeMap, Tolerance, false> DynTree;
+
+  private:
+    
+    const Graph& _graph;
+    const CapacityMap* _capacity;
+
+    Node _source, _target;
+
+    FlowMap* _flow;
+    bool _local_flow;
+
+    IntNodeMap* _level;
+    EdgeNodeMap* _dt_edges;
+    
+    IntNodeMap* _dt_index;
+    DynTree* _dt;
+
+    Tolerance _tolerance;
+    
+    Value _flow_value;
+    Value _max_value;
+
+
+  public:
+
+    typedef DinitzSleatorTarjan Create;
+
+    ///\name Named template parameters
+
+    ///@{
+
+    template <typename _FlowMap>
+    struct DefFlowMapTraits : public Traits {
+      typedef _FlowMap FlowMap;
+      static FlowMap *createFlowMap(const Graph&) {
+	throw UninitializedParameter();
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// FlowMap type
+    ///
+    /// \ref named-templ-param "Named parameter" for setting FlowMap
+    /// type
+    template <typename _FlowMap>
+    struct DefFlowMap 
+      : public DinitzSleatorTarjan<Graph, CapacityMap, 
+			      DefFlowMapTraits<_FlowMap> > {
+      typedef DinitzSleatorTarjan<Graph, CapacityMap, 
+			     DefFlowMapTraits<_FlowMap> > Create;
+    };
+
+    template <typename _Elevator>
+    struct DefElevatorTraits : public Traits {
+      typedef _Elevator Elevator;
+      static Elevator *createElevator(const Graph&, int) {
+	throw UninitializedParameter();
+      }
+    };
+
+    /// @}
+
+    /// \brief \ref Exception for the case when the source equals the target.
+    ///
+    /// \ref Exception for the case when the source equals the target.
+    ///
+    class InvalidArgument : public lemon::LogicError {
+    public:
+      virtual const char* what() const throw() {
+	return "lemon::DinitzSleatorTarjan::InvalidArgument";
+      }
+    };
+
+    /// \brief The constructor of the class.
+    ///
+    /// The constructor of the class. 
+    /// \param graph The directed graph the algorithm runs on. 
+    /// \param capacity The capacity of the edges. 
+    /// \param source The source node.
+    /// \param target The target node.
+    DinitzSleatorTarjan(const Graph& graph, const CapacityMap& capacity,
+			Node source, Node target)
+      : _graph(graph), _capacity(&capacity),
+	_source(source), _target(target),
+	_flow(0), _local_flow(false),
+	_level(0), _dt_edges(0),
+	_dt_index(0), _dt(0),
+	_tolerance(), _flow_value(), _max_value()
+    {
+      if (_source == _target) {
+	throw InvalidArgument();
+      }
+    }
+
+    /// \brief Destrcutor.
+    ///
+    /// Destructor.
+    ~DinitzSleatorTarjan() {
+      destroyStructures();
+    }
+
+    /// \brief Sets the capacity map.
+    ///
+    /// Sets the capacity map.
+    /// \return \c (*this)
+    DinitzSleatorTarjan& capacityMap(const CapacityMap& map) {
+      _capacity = &map;
+      return *this;
+    }
+
+    /// \brief Sets the flow map.
+    ///
+    /// Sets the flow map.
+    /// \return \c (*this)
+    DinitzSleatorTarjan& flowMap(FlowMap& map) {
+      if (_local_flow) {
+	delete _flow;
+	_local_flow = false;
+      }
+      _flow = &map;
+      return *this;
+    }
+
+    /// \brief Returns the flow map.
+    ///
+    /// \return The flow map.
+    const FlowMap& flowMap() {
+      return *_flow;
+    }
+
+    /// \brief Sets the source node.
+    ///
+    /// Sets the source node.
+    /// \return \c (*this)
+    DinitzSleatorTarjan& source(const Node& node) {
+      _source = node;
+      return *this;
+    }
+
+    /// \brief Sets the target node.
+    ///
+    /// Sets the target node.
+    /// \return \c (*this)
+    DinitzSleatorTarjan& target(const Node& node) {
+      _target = node;
+      return *this;
+    }
+
+    /// \brief Sets the tolerance used by algorithm.
+    ///
+    /// Sets the tolerance used by algorithm.
+    DinitzSleatorTarjan& tolerance(const Tolerance& tolerance) const {
+      _tolerance = tolerance;
+      if (_dt) {
+	_dt.tolerance(_tolerance);
+      }
+      return *this;
+    } 
+
+    /// \brief Returns the tolerance used by algorithm.
+    ///
+    /// Returns the tolerance used by algorithm.
+    const Tolerance& tolerance() const {
+      return tolerance;
+    } 
+
+  private:
+        
+    void createStructures() {
+      if (!_flow) {
+	_flow = Traits::createFlowMap(_graph);
+	_local_flow = true;
+      }
+      if (!_level) {
+	_level = new LevelMap(_graph);
+      }
+      if (!_dt_index && !_dt) {
+	_dt_index = new IntNodeMap(_graph);
+	_dt = new DynTree(*_dt_index, _tolerance);
+      }
+      if (!_dt_edges) {
+	_dt_edges = new EdgeNodeMap(_graph);
+      }
+      _max_value = _dt->maxValue();
+    }
+
+    void destroyStructures() {
+      if (_local_flow) {
+	delete _flow;
+      }
+      if (_level) {
+	delete _level;
+      }
+      if (_dt) {
+	delete _dt;
+      }
+      if (_dt_index) {
+	delete _dt_index;
+      }
+      if (_dt_edges) {
+	delete _dt_edges;
+      }
+    }
+
+    bool createLayeredGraph() {
+
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	_level->set(n, -2);
+      }
+      
+      int level = 0;
+
+      std::vector<Node> queue;
+      queue.push_back(_target);
+      _level->set(_target, level);
+      
+      while ((*_level)[_source] == -2 && !queue.empty()) {
+	std::vector<Node> nqueue;
+	++level;
+	
+	for (int i = 0; i < int(queue.size()); ++i) {
+	  Node n = queue[i];
+	  
+	  for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
+	    Node v = _graph.target(e);
+	    if ((*_level)[v] != -2) continue;
+	    Value rem = (*_flow)[e];
+	    if (!_tolerance.positive(rem)) continue;
+	    _level->set(v, level);
+	    nqueue.push_back(v);
+	  }
+
+	  for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
+	    Node v = _graph.source(e);
+	    if ((*_level)[v] != -2) continue;
+	    Value rem = (*_capacity)[e] - (*_flow)[e];
+	    if (!_tolerance.positive(rem)) continue;
+	    _level->set(v, level);
+	    nqueue.push_back(v);
+	  }
+
+	}
+	queue.swap(nqueue);
+      }
+      
+      return (*_level)[_source] != -2;
+    }
+
+    void initEdges() {
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	_graph.firstOut((*_dt_edges)[n], n);
+      }
+    }
+        
+    
+    void augmentPath() {
+      Value rem;
+      Node n = _dt->findCost(_source, rem);
+      _flow_value += rem;
+      _dt->addCost(_source, - rem);
+
+      _dt->cut(n);
+      _dt->addCost(n, _max_value);
+
+      Edge e = (*_dt_edges)[n];
+      if (_graph.source(e) == n) {
+	_flow->set(e, (*_capacity)[e]);
+	
+	_graph.nextOut(e);
+	if (e == INVALID) {
+	  _graph.firstIn(e, n);
+	}
+      } else {
+	_flow->set(e, 0);
+	_graph.nextIn(e);
+      }
+      _dt_edges->set(n, e);
+
+    }
+
+    bool advance(Node n) {
+      Edge e = (*_dt_edges)[n];
+      if (e == INVALID) return false;
+
+      Node u;
+      Value rem;      
+      if (_graph.source(e) == n) {
+	u = _graph.target(e);
+	while ((*_level)[n] != (*_level)[u] + 1 || 
+	       !_tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
+	  _graph.nextOut(e);
+	  if (e == INVALID) break;
+	  u = _graph.target(e);
+	}
+	if (e != INVALID) {
+	  rem = (*_capacity)[e] - (*_flow)[e];
+	} else {
+	  _graph.firstIn(e, n);
+	  if (e == INVALID) {
+	    _dt_edges->set(n, INVALID);
+	    return false;
+	  }
+	  u = _graph.source(e);
+	  while ((*_level)[n] != (*_level)[u] + 1 ||
+		 !_tolerance.positive((*_flow)[e])) {
+	    _graph.nextIn(e);
+	    if (e == INVALID) {
+	      _dt_edges->set(n, INVALID);
+	      return false;
+	    }
+	    u = _graph.source(e);
+	  }
+	  rem = (*_flow)[e];
+	}
+      } else {
+	u = _graph.source(e);
+	while ((*_level)[n] != (*_level)[u] + 1 ||
+	       !_tolerance.positive((*_flow)[e])) {
+	  _graph.nextIn(e);
+	  if (e == INVALID) {
+	    _dt_edges->set(n, INVALID);
+	    return false;
+	  }
+	  u = _graph.source(e);
+	}
+	rem = (*_flow)[e];
+      }
+
+      _dt->addCost(n, - std::numeric_limits<Value>::max());
+      _dt->addCost(n, rem);
+      _dt->link(n, u);
+      _dt_edges->set(n, e);
+      return true;
+    }
+
+    void retreat(Node n) {
+      _level->set(n, -1);
+      
+      for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
+	Node u = _graph.target(e);
+	if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) {
+	  Value rem;
+	  _dt->findCost(u, rem);
+	  _flow->set(e, rem);
+	  _dt->cut(u);
+	  _dt->addCost(u, - rem);
+	  _dt->addCost(u, _max_value);
+	}
+      }
+      for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
+	Node u = _graph.source(e);
+	if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) {
+	  Value rem;
+	  _dt->findCost(u, rem);
+	  _flow->set(e, (*_capacity)[e] - rem);
+	  _dt->cut(u);
+	  _dt->addCost(u, - rem);
+	  _dt->addCost(u, _max_value);
+	}
+      }
+    }
+
+    void extractTrees() {
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	
+	Node w = _dt->findRoot(n);
+      
+	while (w != n) {
+      
+	  Value rem;      
+	  Node u = _dt->findCost(n, rem);
+
+	  _dt->cut(u);
+	  _dt->addCost(u, - rem);
+	  _dt->addCost(u, _max_value);
+	  
+	  Edge e = (*_dt_edges)[u];
+	  _dt_edges->set(u, INVALID);
+	  
+	  if (u == _graph.source(e)) {
+	    _flow->set(e, (*_capacity)[e] - rem);
+	  } else {
+	    _flow->set(e, rem);
+	  }
+	  
+	  w = _dt->findRoot(n);
+	}      
+      }
+    }
+
+
+  public:
+    
+    /// \name Execution control The simplest way to execute the
+    /// algorithm is to use the \c run() member functions.
+    /// \n
+    /// If you need more control on initial solution or
+    /// execution then you have to call one \ref init() function and then
+    /// the start() or multiple times the \c augment() member function.  
+    
+    ///@{
+
+    /// \brief Initializes the algorithm
+    /// 
+    /// It sets the flow to empty flow.
+    void init() {
+      createStructures();
+
+      _dt->clear();
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        _dt->makeTree(n);
+        _dt->addCost(n, _max_value);
+      }
+
+      for (EdgeIt it(_graph); it != INVALID; ++it) {
+        _flow->set(it, 0);
+      }
+      _flow_value = 0;
+    }
+    
+    /// \brief Initializes the algorithm
+    /// 
+    /// Initializes the flow to the \c flowMap. The \c flowMap should
+    /// contain a feasible flow, ie. in each node excluding the source
+    /// and the target the incoming flow should be equal to the
+    /// outgoing flow.
+    template <typename FlowMap>
+    void flowInit(const FlowMap& flowMap) {
+      createStructures();
+
+      _dt->clear();
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        _dt->makeTree(n);
+        _dt->addCost(n, _max_value);
+      }
+
+      for (EdgeIt e(_graph); e != INVALID; ++e) {
+	_flow->set(e, flowMap[e]);
+      }
+      _flow_value = 0;
+      for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
+        _flow_value += (*_flow)[jt];
+      }
+      for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
+        _flow_value -= (*_flow)[jt];
+      }
+    }
+
+    /// \brief Initializes the algorithm
+    /// 
+    /// Initializes the flow to the \c flowMap. The \c flowMap should
+    /// contain a feasible flow, ie. in each node excluding the source
+    /// and the target the incoming flow should be equal to the
+    /// outgoing flow.  
+    /// \return %False when the given flowMap does not contain
+    /// feasible flow.
+    template <typename FlowMap>
+    bool checkedFlowInit(const FlowMap& flowMap) {
+      createStructures();
+
+      _dt->clear();
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        _dt->makeTree(n);
+        _dt->addCost(n, _max_value);
+      }
+
+      for (EdgeIt e(_graph); e != INVALID; ++e) {
+	_flow->set(e, flowMap[e]);
+      }
+      for (NodeIt it(_graph); it != INVALID; ++it) {
+        if (it == _source || it == _target) continue;
+        Value outFlow = 0;
+        for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) {
+          outFlow += (*_flow)[jt];
+        }
+        Value inFlow = 0;
+        for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) {
+          inFlow += (*_flow)[jt];
+        }
+        if (_tolerance.different(outFlow, inFlow)) {
+          return false;
+        }
+      }
+      for (EdgeIt it(_graph); it != INVALID; ++it) {
+        if (_tolerance.less((*_flow)[it], 0)) return false;
+        if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false;
+      }
+      _flow_value = 0;
+      for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
+        _flow_value += (*_flow)[jt];
+      }
+      for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
+        _flow_value -= (*_flow)[jt];
+      }
+      return true;
+    }
+
+    /// \brief Executes the algorithm
+    ///
+    /// It runs augmenting phases by adding blocking flow until the
+    /// optimal solution is reached.
+    void start() {
+      while (augment());
+    }
+
+    /// \brief Augments the flow with a blocking flow on a layered
+    /// graph.
+    /// 
+    /// This function builds a layered graph and then find a blocking
+    /// flow on this graph. The number of the levels in the layered
+    /// graph is strictly increasing in each augmenting phase
+    /// therefore the number of the augmentings is at most \f$ n-1
+    /// \f$.  The length of each phase is at most \f$ O(m \log(n))
+    /// \f$, that the overall time complexity is \f$ O(nm \log(n)) \f$.
+    /// \return %False when there is not residual path between the
+    /// source and the target so the current flow is a feasible and
+    /// optimal solution.
+    bool augment() {
+      Node n;
+
+      if (createLayeredGraph()) {
+	
+	Timer bf_timer;
+	initEdges();
+
+	n = _dt->findRoot(_source);
+	while (true) {
+	  Edge e;
+	  if (n == _target) {
+	    augmentPath();
+	  } else if (!advance(n)) {
+	    if (n != _source) {
+	      retreat(n);
+	    } else {
+	      break;
+	    }
+	  }
+	  n = _dt->findRoot(_source);
+	}     
+	extractTrees();
+
+	return true;
+      } else {
+	return false;
+      }
+    }
+    
+    /// \brief runs the algorithm.
+    /// 
+    /// It is just a shorthand for:
+    ///
+    ///\code 
+    /// ek.init();
+    /// ek.start();
+    ///\endcode
+    void run() {
+      init();
+      start();
+    }
+
+    /// @}
+
+    /// \name Query Functions
+    /// The result of the %Dijkstra algorithm can be obtained using these
+    /// functions.\n
+    /// Before the use of these functions,
+    /// either run() or start() must be called.
+    
+    ///@{
+
+    /// \brief Returns the value of the maximum flow.
+    ///
+    /// Returns the value of the maximum flow by returning the excess
+    /// of the target node \c t. This value equals to the value of
+    /// the maximum flow already after the first phase.
+    Value flowValue() const {
+      return _flow_value;
+    }
+
+
+    /// \brief Returns the flow on the edge.
+    ///
+    /// Sets the \c flowMap to the flow on the edges. This method can
+    /// be called after the second phase of algorithm.
+    Value flow(const Edge& edge) const {
+      return (*_flow)[edge];
+    }
+
+    /// \brief Returns true when the node is on the source side of minimum cut.
+    ///
+
+    /// Returns true when the node is on the source side of minimum
+    /// cut. This method can be called both after running \ref
+    /// startFirstPhase() and \ref startSecondPhase().
+    bool minCut(const Node& node) const {
+      return (*_level)[node] == -2;
+    }
+
+    /// \brief Returns a minimum value cut.
+    ///
+    /// Sets \c cut to the characteristic vector of a minimum value cut
+    /// It simply calls the minMinCut member.
+    /// \retval cut Write node bool map. 
+    template <typename CutMap>
+    void minCutMap(CutMap& cutMap) const {
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+	cutMap.set(n, (*_level)[n] == -2);
+      }
+      cutMap.set(_source, true);
+    }    
+
+    /// @}
+
+  };
+}
+
+#endif